Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9b9)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a9b9.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(9/2), 19/4}, -z] == (1/(206158430208 z^(15/4))) (11 (Sqrt[Pi] (-1154218440375 - 305247852000 z - 60147360000 z^2 - 17108582400 z^3 + 9776332800 z^4 - 736100352 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-384739480125 + 74131621200 z - 1960358400 z^2 + 620077056 z^3 - 46202880 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (1154218440375 - 925918484400 z + 47226816000 z^2 + 658022400 z^3 - 46989312 z^4 + 1048576 z^5) Sin[2 Sqrt[z]])))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]